Consider a finite set A and $n\ge 1$. We study complete simulation of transformations of $A^n$, also known as automata networks. For $m\ge n$, a transformation of $A^m$ is n-complete of size m if it may simulate every transformation of $A^n$ by updating one register at a time. Using tools from memoryless computation, we establish that there is no n-complete transformation of size n, but there is one of size $n+1$. By studying various constructions, we conjecture that the maximal time of simulation of any n-complete transformation is at least 2n. We also investigate the time and size of sequentially n-complete transformations, which may simulate every finite sequence of transformations of $A^n$. Finally, we show that there is no n-complete transformation updating all registers in parallel, but there exists one updating all but one register in parallel. This illustrates the strengths and weaknesses of sequential and parallel models of computation.

考虑一个有限集A和$ñ\ge \mathrm{1个}$。我们研究完全模拟的变换${\mathrm{一种}}^{ñ}$，也称为自动机网络。对于$米\ge ñ$，是 ${\mathrm{一种}}^{米}$是Ñ -complete的大小米，如果它可以模拟的每一个变换${\mathrm{一种}}^{ñ}$通过一次更新一个寄存器。从记忆计算使用的工具，我们确定没有ň大小的-complete改造ñ，但有大小之一$ñ+\mathrm{1个}$。通过研究各种结构，我们推测，任何n个完全变换的仿真最大时间至少为2 n。我们还研究了顺序n个完全转换的时间和大小，它们可以模拟的每个有限转换序列。${\mathrm{一种}}^{ñ}$。最后，我们表明没有n完全转换并行更新所有寄存器，但是存在一个并行更新除一个寄存器之外的所有寄存器。这说明了顺序和并行计算模型的优缺点。